Introduction

Many
of the articles on this Web site are versions of the Fermi Problem described
in the first section. Others are essays - some short, some long. Some
are merely attempts to come to terms with basic concepts, such as the
'size' of the speed of light or the number 'one trillion'. Others discuss
more advanced concepts. The last few essays involve college-level physics,
and might be difficult for those who have not taken at least some introductory
courses. The essays discussing the gravitational field energy density
and the thermodynamic four-vector are speculative and invite comments
from you, the reader.

The
energy density article was written to fill a gap, which I noted in books
on Special Relativity. Of the three classical problems of General Relativity,
two (the deflection of starlight and the gravitational red shift) are
routinely presented as exercises with a discussion of similarities and
differences with General Relativity; the third (the rotation of perihelion)
seems never to be touched at this level. This article is an attempt
to rectify this situation. The four-vector article arises from the observation
that components of a four-vector satisfy a continuity equation. Einstein
used this idea in his early writing on Special Relativity when introducing
the current density four-vector. I have raised the question as to whether
similar logic might apply to thermodynamics when the heat conduction
equation and the thermal diffusion equation are combined to form a continuity
equation.

The
earlier pieces are nowhere near so involved, and require only a little
number skill and, possibly, some high school algebra. Enrico Fermi,
the theoretical physicist of Manhattan Project fame, knew only too well
that physicists are often confronted by situations in which they are
forced to reason from minimal information. He, therefore, taught his
students how to think about complicated sounding problems by using everyday
knowledge. The 'Piano Tuner' is typical: "If 3,000,000 people live in
Chicago, then how many of them are piano tuners?"

There
are many cases in science, and even in everyday life, when we encounter
seemingly insolvable problems such as this. So the problems presented
here provide an opportunity to practice with Fermi's approach. Some
of the problems are of my own invention. Others came from students or
people I met when conducting public lectures. Some are simple, others,
complex. Each problem has, of course, a rigorous solution, although
the solutions presented here make no pretense at rigor! Consider them
'back-of-the-envelope' calculations - estimates, ballpark solutions.
In so doing, you will gain valuable insight into a technique much used
by professionals.